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NEET 2015
Exam
NEET
Year
2015
Subject
Physics
Chapter
Work, Power and Energy

NEET 2015 · Physics · Work, Power and Energy

A block of mass 10kg , moving in x direction with a constant speed...

A block of mass 10kg10kg, moving in xx direction with a constant speed of 10ms−110m{s}^{- 1} , is subjected to a retarding force F=[(0.1)x]Jm−1F = \left[( 0 .1 )x\right]J{m}^{- 1} during its travel from x=20mx = 20m to 30m30m . Its final kinetic energy will be:

Options

  1. A475J475J
  2. B450J450J
  3. C275J275J
  4. D250J250J

Correct answer

A. 475J475J

Step-by-step solution

m=10kg,u=10ms−1m = 10kg, u = 10m{s}^{- 1}

Final KE will be given by

KEf=KEi+WK{E}_{f} = K{E}_{i} + W

=12mu2+∫2030(−0.1x)dx= \dfrac{1}{2}m{u}^{2} + \mathop{∫}_{20}^{30}\left(- 0 .1 x\right)dx

=12×10×100+(−0.1)[x22]2030= \dfrac{1}{2} \times 10 \times 100 + \left(- 0.1\right){\left[\dfrac{{x}^{2}}{2}\right]}_{20}^{30}

=500+(−0.1)2(900−400)= 500 + \dfrac{\left(- 0.1\right)}{2}\left(900 - 400\right)

KEf=500+(−0.1)5002K{E}_{f} = 500 + \dfrac{\left(- 0.1\right)500}{2}=475J= 475J
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